Cryptography is beginning to pervade all walks of human life for secure cyber transactions. The classical method for encryption/decryption is either asymmetric RSA encryption/decryption (which takes tens of millions of computer cycles per encryption/decryption) or symmetric block ciphers such as NIST standard AES.
Conventional block ciphers ([12, 13]) derive their security from an embedded secret, more commonly referred to as a key. One of the inputs, key, in each round is a secret, whereas the round functions themselves are public. This is a deliberate design decision so that the algorithm can be published as a standard. The secret, however, is combined with the state in a limited way, as an xor, during a round. The xor based mixing of the cipher state and the secret leads to some vulnerabilities based on linear and differential cryptanalysis. The complexity of extracting the secret or its properties is proportional to the non-linearity, among many other attributes, of the round functions.
The prior work abstract the process of encryption in finite field algebra (Galois fields), and then develops hardware/software implementation algorithms. Such indirection causes it to be relatively slower. The security properties are derived from S-boxes that are proved to be non-linear. However, the secret does not participate in S-boxes. Such public knowledge of S-box constants allows for an adversary to develop static statistical models. The secret is merely XORed with the plaintext.
Therefore, there is a need for improvements in cryptography.